AN EMPIRICAL INVESTIGATION INTO THE BEHAVIOR OF OPTIONS AROUND MERGER AND ACQUISITION ANNOUNCEMENTS By JAMES A. YODER A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1988 OF F LIB ACKNOWLEDGEMENTS I would like to express my special thanks to the chairman of my committee, Haim Levy, and to Drs. Roger Huang, Roy Crum and Sandy Berg. T would also like to express my appreciation to Drs. Andy McCollough, Craig Tapely, Robert Radcliffe, Dave Brown and Joel Houston for their encouragement and support. I would also like to express my gratitude to my fellow students Young Hoon Byun, Lesa Nix, Bruce Kuhlman and Neil Sicherman for their suggestions and technical assistance. I would also like to acknowledge the computer programming assistance of Eric Olson. 11 TABLE OF CONTENTS Page ACKNOWLEDGMENTS . . a ABSTRACT v CHAPTERS 1 INTRODUCTION 1 The Behavior of Option Prices Around Merger Announcements 2 The Behavior of Implied Standara Deviations Around Merger Announcements 4 Does the Option Market React to Merger/Acquisition Activity Differently than the Equity Market? 5 How Does an Event Study in the Option Market Differ From One in the Equity Marker? ......... 8 2 REVIEW OF THE LITERATURE 12 Mergers 12 Options 16 Pricing 16 Option Market Efficiency 18 Variance Bias in the Black-Scholes Model 19 3 THE BEHAVIOR OF OPTIONS AND OPTION MARKETS AROL^ND MERGER AND ACQUISITION ANNOUNCEMENTS ... 20 Data 20 The Behavior of Options Around Merger and Acquisition Announcements 22 The Behavior of ISDs Around Merger and Acquisition Announcments 24 Methodology ..... 26 Interpretation Results 29 The Behavior of Call Option Prices Around Merger and and Acquisition Announcements 34 Methodology and Results 36 Interpretation Results 40 The Behavior of Options Around Merger and Acquisition Announcements 43 Methods and Results 47 Methods and Results 50 1X1 4 VAEIANCE BIAS AND NON- SYNCHRONOUS PRICES IN THE BLACK- SCHOLES MODEL 60 Variance Bias in the Black-Scholes Model 61 Methodology and Results 64 Non- synchronous Prices and the Black-Scholes Model .... 71 Methodology and Results 72 Conclusion 77 5 SUMMARY AND CONCLUSIONS 79 REFERENCES 83 BIOGRAPHICAL SKETCH 87 IV Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy AN EMPIRICAL INVESTIGATION INTO THE BEHAVIOR OF OPTIONS AROUND MERGER AND ACQUISITION ANNOUNCEMENTS By James A. Yoder December 1988 Chairman: Haim Levy Major Department: Finance, Insurance, and Real Estate This dissertation exam.ines the behavior of options around merger and acquisition announcements. A variation of the traditional event study methodology was applied to the option market in order to measure the abnormal returns accruing to the bidding firm and target firm optionholders. The event study was extended to the equity market for comparison purposes. The behavior of ISDs was also examined in order to determine whether the option or equity market first reacted to the merger/acquisition announcement and to decompose the abnormal returns in the option market into a component due to changing stock prices and a component due to changing stock volatilities. Some methodological issues involving event studies were also examined. CHAPTER 1 INTRODUCTION Two of the most important developments in finance in recent years have been the growth of option markets and the high level of merger and acquisition activity. Not surprisingly, both of these areas have been subject to intense academic scrutiny. Literally hundreds of articles have been published on the theory and applications of options. There are also numerous papers concerned with the rationale for mergers and their impact on stockholders' wealth. This dissertation attempts to relate these two subjects through an examination of oprion and option market behavior around merger and acquisition announcements. In order to accomplish this, four major issues will be addressed: 1. How do option prices react around merger/acquisition announcements ? 2. How do the Implied Standard Deviations (ISDs) of options react around merger and acquisition announcements? 3. Does the option market react to merger and acquisition activity differently than the equity market? A. How does an event study in the option market differ from one in the equity market? Each of these issues will be discussed in turn. The Behavior of Option Prices Around Merger Announcements Researchers in the equity market have sought to determine whether mergers and acquisitions produce economic gains and, if so, who reaps the benefits. Their findings have been relatively consistent. Dodd (1980), Asquith (1983) and Eckbo (1983), for example, have all presented evidence on the effects of mergers on shareholders' wealth. They conclude that most of the gains are captured by the stockholders of the target firm. Gains to the bidding firm shareholders are small and possibly non-existent. Their estimates of the abnormal returns accruing to the bidding firm shareholders for the two days prior to the announcement range from a -1.09 percent loss to a paltry 0.20 percent gain. For the target firm shareholders, however, statistically signif- icant gains ranging from 6.20 percent to 13.41 percent were obtained. The merger literature is discussed more thoroughly in Chapter 2. These results in the equity market lead to empirically testable hypotheses for the expected behavior of options around merger and acquisition announcem.ents . Under the assumption that the option market !s efficient, option prices (and ISDs) can be expected to react prior to the formal merger announcement and stabilize immediately afterward. Merger negotiations involve many people such as investment bankers, lawyers, administrative personnel, etc. Word of impending mergers :!eaking to the financial market place has been amply demonstrated in the equity market. There is no reason why the same phenomenon should not occur in the option market. A second hypothesis is that abnormal returns to the target firm optionholders should exceed those of the bidding firm optionholders. Theoretically, a call option can be duplicated by an appropriately selected stock-bond portfolio. Because of this, the wealth effects of merger and acquisition announcements on optionholders can be expected to mirror that of the equityholders. The wealth effects of merger and acquisition activity on option- holders is of interest for a number of reasons. In a recent survey article of the market for corporate control literature, Jensen and Ruback (1983) identified six key questions that have been addressed. At the top of the list is the following = "How large are the gains to shareholders of bidding and target firms?" Options by their very nature afford superior leverage to the underlying equity. Consequently, optionholders, per dollar invested, have more reason to be concerned with potential merger and acquisition activity than the equityholders. An analysis of option prices around merger and acquisition announce- ments may also shed light on a puzzling question. Merger activity is widespread but the rationale for it is not clear. As noted earlier, gains to the bidding firm shareholders are small and possibly negative. Why then do managers undertake merger and acquisition programs if they do not benefit the shareholders? An examination of bidding firm option prices may help to resolve this issue, An option can be interpreted as a leveraged position in the equity. This leverage aspect of options may make them more sensitive to events than the underlying equity. Small abnormal returns in the equity market might result in much larger abnormal returns in the option market. Thus, it may be easier from a statistical standpoint to determine if bidding firm stockholders benefit from merger/acquisition activity by looking at the behavior of associated option prices. The Behavior of Implied Standard Deviations Around Merger Announcements The behavior of ISDs around merger announcements is important for two reasons. First, it is inseparable from the price behavior of options. Stock volatility is one of the input variables for the Black- Scholes model. By examining the ISD, it is possible to decompose changes in option prices into a component due to price changes in the underlying stock and a component due to changes in the underlying volatility. Second, it provides an alternative measure of the informa- tion content associated with merger and acquisition announcements. Numerous studies have attempted to measure the information content of accounting announcements by showing that the expected return of the stock is affected. Patell and Wolfson (1979, 19Sl) have pointed out that other moments of stock price distribution may also be affected by the announcement and thus serve as a measure of its significance. They proceeded to use ISDs as an ex-ante measure of the information content associated with earnings announcements whose disclosure date is known. This dissertation attempts to use ISDs to measure the expected impact of merger and acquisition announcements which are totally or at best partially anticipated events. The hypotheses concerning the behavior of ISDs around merger and acquisition announcements parallels that of option prices. The first hypothesis is that ISDs should react prior to the formal announcement and stabilize immediately afterward. The second hypothesis is that the change in ISDs for the target firm should exceed that of the bidding ''irm options. Merger and acquisition activity has very little impact on the bidding firm shareholders. Thus, the distribution of stock returns should not significantly change as a result of the announce- ment. The target firm shareholders, however, are greatly affected by the merger and acquisition activity. Increased volatility of the underlying stock returns can be generated by a multitude of factors. Uncertainty, for example, can arise over the anticipated terms of the agreement, whether a competing offer will be made or even whether the deal will be consummated. Does the Option Market React to Merger and Acquisition Activity Differently than the Equity Market? The third major area of inquiry in this dissertation is the relationship between the option and equity markets around merger announcements. There are two independent arguments for hypothesizing that the merger activity will be more strongly manifested in the option rather than the equity market prior to the announcement. Options represent leveraged positions in the underlying equity. The beta of an option in the Black-Scholes framework is always greater than that of the stock. Because of this, the option market may be more sensitive to events than the equity market. Even though the two markets may be reacting to the same information, the signal may first be more apparent and stronger in the option market. It is also possible that the option market contains information that is not incorporated in the equity market prior to mergers. As mentioned previously, a call or put option can be duplicated by an appropriate stock-bond portfolio. Because of this, options have been viewed as "derivative" assets whose prices are completely determined by the underlying equity. The possibility that the option market may influence the equity market has received little attention. It is conceivable that information is first processed in the option market and then filters to the equity market. A similar issue has been studied by Manaster and Rendleman (1982). They have advanced the intriguing hypothesis that the option market may play a key role in determining equilibrium stock prices. They argue that some investors may prefer to invest in the option rather than the equity market because of reduced transaction costs, fewer short selling restrictions, and most importantly, superior leverage. These traders could push option prices out of equilibrium relative to the underlying stocks. Arbitrageurs would then intervene to restore equilibrium between the two markets. Manaster and Rendleman attempted to test their theory. They "inverted" the Black-Scholes model to solve for the implied stock price. The implied stock price was then used to predict future stock prices. They found some evidence that the option market contains information that is not incorporated in the equity market. Unfor- tunately, their results are very weak and fatally flawed by their reliance on non- synchronous data. The data used in this dissertation will avoid this problem. In retrospect, Manaster and Rendlemans ' lack of results is not surprising. Both the option and equity markets react to public information. Generally, one would expect both markets to adjust simultaneously to new public information. On any given day for any particular corporation there may not be and probably is not information that is not fully reflected in both markets. However, this may not be true prior to major announcements by corporations such as mergers. In the case of mergers, the option market could be expected to be particularly influential in determining stock prices around merger announcements. Keown and Pinkerton (1981) have argued that information concerning impending mergers is suscep- tible to insider exploitation due to the large number of people typically involved in the negotiating process. They have attributed increased trading volume before the merger announcement to insider activity. An insider attempting to profit from knowledge of an impend- ing merger would have an incentive to use options because of their leverage aspects. To quote Fischer Black (1975, p. 61), "Since an investor can usually get more action from a given investment in options than he can by investing in the common stock, he may choose to deal with options when he feels he has an especially important piece of information." Option prices can be expected to contain more informa- tion than the equity market if nonpublic information is being exploited. If information regarding future mergers first reaches the financial markets through insider trading in options, merger activity may very well be reflected in the option market before the stock market. A separate issue raised by the above argument is that the option market m.ay make the equity market more efficient. If the option market serves to bring nonpublic information into the financial markets and options influence the prices of the underlying stock, then stocks with listed options should respond sooner to impending m.ergers than similar stocks without options. How Does an Event Study in the Option Market Differ From One in the Equitv Market? An event study attempts to measure the impact of some event on securityholders by comparing actual returns around the announcement to those predicted by some model. These predicted returns should be the returns that would have occurred if the event (merger and acquisitions in this case) had not taken place. The difference between the actual and predicted returns is the basic measure of the impact of the event. These residuals are then aggregated to measure the total impact of the event and provide statistics for tests of significance. In the equity market, predicted returns are usually generated by one of two models: a. Market model b. Mean returns The market model assumes there is a linear relationship between individual security returns and market returns: Kit = a^ + 3iRmt Where R^^ = return on company i for day t -R-nit = return on the market for day t The coefficients a and are obtained by regressing the company returns against the market returns over some base period prior to the merger activity. The base period should be selected so that the company returns are not affected by the event activity. .'\nother approach to generating predicted returns is to simply use the mean returns on the individual security computed over some base period _ n R^ = 1/N 2 R,;t where R^ = mean return on company i Rj_f = return of company i for day t N = number of observations in the base period Again the base period should be selected so that the event activity has no effect. Two implicit assumptions underlie the traditional event study methodology in the equity market. The first is that the return generating process is linear. As long as predicted returns equal actual returns on average, the residuals should average out to zero over a large enough cross-sectional sample in the absence of some conimon disturbing event. The same reasoning justifies parameter estimation for the two models. The true beta is unknown and must be estimated. The estimated beta may lie above or below the true value. As long as an unbiased of beta is used, however, deviations from the true beta return will average out to zero. Since these models are linear, deviations from the true expected return will also offset and residuals should average out to zero in the absence of a common disturbance. The second assumption is that the return generating process is stationary. Specifically, beta is assumed to remain constant over time. Call prices in a Black-Scholes framework are a function of five input variables. Two of these, the stock price and its volatility, are company specific and would be affected by an event such as a merger acquisition announcement. One implication of this is that there may be 10 a subtle but important difference between the interpretation of the results of an event study in the option and equity markets. i-!e.tger activity may not benefit a stockholder even if abnormal returns are observed. These abnormal returns may be accompanied by increased risk. This increased risk may not be desired by an investor with a small portfolio even if it is compensated for by larger expected (not realized) returns. If an investor holds a call option, the situation may be entirely different. An increase in the volatility of the underlying srock would definitely be preferred by all investors. Increased volatility would result in an actual (not expected) increase in the call price. The reason for this is that the return generating process underlying call prices is based on the formation of risk-less hedged portfolios. The Black-Scholes formula is by far the most widely used option pricing model. Using it to generate predicted returns for an event study, however, presents some technical problems. The Black-Scholes model is highly non-linear. Consequently, using sample estimates for the input variables may result in a systematic bias. Errors in estimat- ing the variables may offset in a large sample. Equal deviations from the true parameter estimate, however, will not result in equal devia- tions from the true call price. The most crucial variable is the stock volatility since the Black-Scholes model is most sensitive to it. Because of this problem, the results of an event study utilizing the Black-Scholes model must be interpreted with care. A simulation analysis, however, provides some m.easure of the magnitude of this effect. The Black-Scholes formula was used to generate a theoretical option price assuming true values for the input parameters. Sample 11 estimates of the volatility were generated for input into the Black- Scholes model. These sample call prices based on sample estimates for the volatility were compared to the theoretical call value. In general, the difference was small (see chapter A). CHAPTER 2 REVIEW OF THE LITERATURE The literature on option theory and mergers, as mentioned previ- ously, is immense. It is impossible to discuss in detail all the relevant studies in either of these fields. At best, the most impor- tant results can only be highlighted. This section will give a brief review of the work that directly affects this dissertation. The literature dealing with the impact of mergers on shareholders wealth, option pricing, option market efficiency, and variance bias in the Black-Scholes model will be addressed in turn. Mergers Two fundamental questions have been raised regarding merger activity. The first is why do mergers occur? In 1985 alone, merger activity involved over $120 billion in assets. Yet the economic justification for all this activity is not obvious. Levy and Sarnat (1970) have shown that given perfect capital markets, pure conglomerate mergers should not create value. Agency theory provides one rationale for the continuous merger activity that has been observed over the past few decades. Levy and Sarnat (1970), Lewellen (1971) and Gali and Masulis (1976) have argued that combining firms with less than perfectly correlated cash flows lowers the chances for bankruptcy. Thus, managers have an incentive to engage in merger activity so as to reduce their employment risk. Reid (1968) has argued that managers strive to maxim.ize the size of the firm 12 13 rather than shareholder wealth. Jensen and Heckling (1976) have pointed that since managers are agents for the stockholders' their interests are not necessarily the same. Others have sought to justify merger activity on the grounds that it produces real economic gains. Mergers may result in more efficient economic units. Weston and Chung (1983) have summarized possible sources of these efficiencies. 1. Differential Efficiency 2. Inefficient Managem.ent (target firm) 3. Operating Synergy A. Financial Synergy 5. Strategic Realignment 6. Undervaluation (target firm) -..- of now, however, the exact rationale for mergers is still an unresolved issue. The second major issue that the merger literature has addressed is what are the effects of mergers on shareholders' wealth? Numerous studies concerned with this issue have appeared since Mandleker's (1974) seminal paper. Most of these have used the well known event study methodology. Event studies in the equity market involving mergers have become relatively standardized. A base period prior to the event is selected, and data from this period are used to estimate predicted returns. The impact of the event is measured by calculating the difference between the actual and predicted returns during some period surrounding the event. The residuals are then aggregated and statistically analyzed, 14 usually using some form of a t-test, to determine if the excess returns are significantly different from zero. Predicted returns in the equity market have usually been generated by one of two models. The first method is to use the market model. Rjt = aj + Bj"R^t The estimates of aj and Bj are obtained by regressing the company returns against the market returns during some base period prior to and presumably untainted by the merger activity. The second method is to simply use the mean return computed over some base period. Brown and Warner (1985) have shown that the event study metho- dology is very robust to the method used to calculate excess returns. Using simulation analysis, they showed that there is very little difference in the returns (or residuals) generated by the two methods. Because of this, mean adjusted returns will be used in this study. Jensen and Ruback (1983) have summarized the results of the more important merger studies concentrating on announcement effects. These results are shown in the table below. The top panel shows the results for the two days prior to the announcement. The bottom panel shows the results for the one month prior to the announcement. In each case, the total return during the event period, the number of observations and the t-statistic is given for both the bidding and target firms. The results are very consistent. The gains to the acquiring firms are positive but small. The target firm stockholders reap much larger returns. This is true for both the short-term (2 day) and long- term (one month) event period. In addition, these results hold for both successful (consummated) and ultimately unsuccessful mergers. 15 Table 2.1 A'Dnormal Returns Associated with Mergers; Sample Size and t-statistic Study Sample Bidding firm Target firm period A. Two-day announcement effects T)odd /0-77 -1.09" +13.41 (1980) (60"", -2. 98""'") (71^23.80) Asquith 62-76 +0.20 +6.20 (1983) (196,0.78) (211,23.07) Eckbo 63-78 +0.07 +6.24 (1983) (102,-0.12) (57,9.97) Weighted excess return -0.05 +7.72 B. One-month announcement effects Eodd 70-77 +0.80 +21.78 (60,0.67) (71,11.93) Asquith 62-76 +0.20 +13.30 (1983) (196,0.25) (211,15.65) Eckbo 63-78 +1.58 +14.08 (1983) (102,1.48) (57,6.97) Asquith et. 63-79 +3.48 +20.5 al. (1983) (170,5.30) (35,9.54) Malatesta 69-74 +0.90 +16.8 (1983) (256,1.53) (83,17.57) weighted excess return +1.37 +15.90 -excess return ""'number of observations " " "t - Stat is t i c 16 The paper by Asquith, Bruner and Mullins deserves additional comment. Schipper and Thompson (1983) have shown that acquisition programs generate excess returns. If this is true, one might expect the impact of successive mergers to diminish. Asquith et. al. compare the abnormal returns associated with the first, second, third, and fourth mergers. They find no evidence that abnormal returns are capitalized in the earlier mergers. They also found that the abnormal returns to the acquiring firm is dependent on the size of the acquired firm. Options Pricing The seminal work on option pricing is, of course, the Black- Scholes option pricing model. Black and Scholes (1973) noted that a call and the underlying stock could be combined to form a risk-free hedged portfolio if continuous rebalancing was possible. This fact, combined with some appropriate assumptions 1. frictionless capital markets 2. risk-free interest rate is constant 3. stock pays no dividends A. stock prices follow an Ito process with constant drift 5. no restrictions on short sales allowed them to derive a differential equation relating call and stock prices. Using stochastic calculus, they solved for the call price yielding the familiar Black-Scholes formula as a result C = SN(d^) - Xe-^T^J(^i^) where 17 d;, = [ln(S X) + (r + 0.5o-)T]/ajT d2 = dT_ - aVT The most limiting of the Black-Scholes restrictions is that the underlying stock pays no dividends. Modifying the model for dividends has two components. First, the stock price must be adjusted for the expected drop on the ex-dividend date. Second, the model must reflect that an American call has value due to its early exercise right. If a dividend is large enough, it may pay to exercise the option immediately before the stock goes ex-dividend. These problems can be dealt with simply by subtracting the present value of future dividends from the stock price as Black (1975) has suggested or assuming that dividends are paid continuously as Merton (1973) has done. Roll (1977), Geske (1979b), and Whaley (1981) have advanced more complex formulation that take both considerations into account. Whaley (1979) has empirically tested the different approaches to dividend adjustment and found the differences were slight. A number of variants and extensions of the Black-Scholes model have appeared. Merton (1973) has relaxed the assumption of stationary interest rates. Thorpe (1973) has examined the effect of short sales restrictions. Geske (1979a) has developed a compound option formula. The effects of different distributional assumptions regarding stock prices have also been investigated. Cox and Ross (1976) have developed a pure jump model that allows for discrete stock price movements. They have also developed a constant elasticity of variance model that allows for the variance to change with the stock price. Merton (1976) has developed a mixed diffusion- jump model that super- imposes a jump process on a continuous return generating process. 18 Despite these advances, the Black-Scholes model with the stock prices adjusted for dividends is still the most widely used by far. Many of the models discussed above are difficult if not impossible to apply. Even if they can be applied, no model has yielded consistent, significantly better results for options near the money. While there are limitations to the Black-Scholes model, there is no strong reason to use any of the more esoteric alternatives in this study. Option Market Efficiency A number of studies have been made of the efficiency of the Chicago Board of Options exchange. These studies are joint tests of market efficiency and the Black-Scholes model. Galai (1977) conducted one of the earliest and most comprehensive studies using the Black- Scholes model to identify mispriced options. He found that statisti- cally (but not economic) significant excess returns could be earned. Chiras and Manaster (1978) adopted a different approach in analyzing option market efficiency. They weighted the ISD of each option on the stock by the option price elasticity to arrive at an overall measure of the stock's future volatility (WISD) . They then compared the WISD as an estimate of future stock volatility to esti- mates based on past stock returns. Having demonstrated the superiority of WISDs, they then proceed to compute imiplied option prices. Under- priced and overpriced options were then identified by comparing implied and actual prices. Risk-free hedges were then formed which earned substantial abnormal returns. These results are in agreement with a similar study by Trippi (1977) which used a simpler weighting scheme to arrive at WISDs. Kalay and Subrahmanyara (1984) have also provided some 19 evidence of option market inefficiency on the ex-dividend day of the equity. Phillips and Smith (1980) have found fault with studies reporting inefficiencies in the option market. They argued that a close examina- tion of trading costs (most notably the bid-ask spread) would account for the abnormal returns reported in earlier studies. Bhattacharya' s (1980) study of CBOE (Chicago Board of Options Exchange) took these costs into consideration. In general, his results were consistent with market efficiency. Variance Bias in the Black-Scholes Model In order to apply the Black-Scholes model, five input variables must be obtained: the stock price, exercise price, time to maturity, risk-free rate of interest and the volatility of the underlying stock. Of these, four are directly observable. Only the variance of the underlying stock returns needs to be estimated. Classical methods of estimating the variance will bias the model. Although unbiased estimators of the variance exist, the Black-Scholes model is highly non-linear. Equal deviations from the true variance will not result in equal deviations from the true call price as Ingersoll (1977) and Merton (1975) have observed. Boyle and Ananthanrayanan (1977) have used numerical integration to examine the magnitude of the expected error in a single case. Butler and Schachter (1986) trace the behavior of this bias to the second derivative of the cumulative normal density function. CHAPTER 3 THE BEHAVIOR OF OPTIONS AND OPTION MARKETS AROUND MERGER AND ACQUISITION ANNOUNCEMENTS This chapter discusses the behavior of options and option markets around merger and acquisition announcements. The impact of merger and acquisition announcements will be studied by examining the behavior of option prices and ISDs around the announcement date. These results will be compared to those obtained from the underlying equity using the traditional event study methodology. The organization of this chapter is as follows. First, the data is described and a potential problem discussed. Next, the behavior of options around merger and acquisition announcements is analyzed. The return of an option is affected by two company specific variables: the stock price and stock volatility. Both of these variables are likely to be affected by merger and acquisition activity and thus influence call returns. An attempt is made to decompose the total impact of merger and acquisition activity into two components. First, the effect of changing ISDs is investigated and then the total impact due to both changing stock prices and stock volatility is analyzed. Finally, the traditional event study methodology is applied to the underlying stock in order to compare the behavior of the two markets. Data The merger and acquisitions selected for this srudy will be obtained from Mergers and Acquisitions . The mergers and acquisitions 20 21 selected will be confined to those involving at least $100 million in assets with either the acquiring or acquired firm having options listed on the CBOE between 1982 and 1985. The reason for this is to ensure the merger and acquisition is an event. Corporations listed on the CBOE tend to be well established firms with large equity bases. The value of all the outstanding stock in firms such as General Motors, General Electric and International Business Machines, for example, is measured in the billions of dollars. The announcement date will come from the Wall Street Journal Index. The Wall Street Journal will also be used to get the bid-asked spread on U.S. Treasury bills in order to calculate the risk-free rate. The risk-free rate for input into Black-Scholes formula will be the yield on the T-bill maturing closest to the expiration date of the option. The yield will be calculated according to the formula below from Cox and Rubinstein (1985, p. 255) r = (F/lG,GOO)'l/t where r = one plus the risk-free rate P = price of a $10,000 T-bill = 10,000 [l-0.01(bid + asked)/2 (n/360)] n = number of days to maturity t = time to maturity expressed in years The critical data for this thesis is the stock and option prices. Closing prices from the Wall Street Journal or similar sources can not be used because of the possibility of nonsynchronous trading between the two markets. Trading in the option market is significantly less active than in the equity market. It is quite likely that the last 22 option trade occurred prior to the last stock trade on any given day. The current stock price for use in the Black-Scholes formula is the price existing at the time the option is being valued. Using the Black-Scholes model to generate predicted returns as in this study requires the stock price at the time of the last option trade. This problem, as Bookstaber (1981) has pointed out, casts doubt on much of the empirical work on options that has been done to date. In order to avoid any problems with nonsynchronous trading, time-stamped data will be used. The Berkeley Options Tape will be the primary source of stock and option price information. Data from Francis Emory Fitch, Inc., although not machine readable, is also suitable. The Behavior of Options Around Merger and Acquisition Announcements The behavior of stocks around merger announcements has been extensively studied (see chapter 2). The results have been very consistent. Most of the gain due to merger activity is captured by the stockholders of the target firm. Gains to the bidding firm share- holders are small and possibly non-existent. These results suggest empirically testable hypotheses for the expected behavior of options around merger and acquisition announce- ments. Market anticipation of formal merger announcements has been observed in the equity markets. Under the assumption that the option market is efficient, option prices and ISDs should react prior to the formal merger and acquisition announcement and stabilize immediately afterward. A second hypothesis is that the abnormal returns to the target firm optionholders should exceed those of the bidding firm 23 optionholders. Theoretically, a call option may be duplicated by an appropriately selected stock-bond portfolio. Because of this, the wealth effects of merger and acquisition announcements can be expected to mirror that of the equityholders. This assumes, however, that other factors such as the stock volatility are not affected by the merger and acquisition activity. There are two main reasons why an analysis of the impact of merger and acquisition activity of optionholders wealth is of interest. First, the methodology used, the traditional event study, has never been applied to the option market. An event study in the option market presents new issues and sheds light, as will be discussed later, on event studies in the equity market. The second major reason why the wealth effects of merger and acquisition activity is important is that options afford superior leverage to the underlying equity by their very nature. Optionholders, per dollar invested, have more reason to be concerned with the effects of merger and acquisition activity than the equityholders . These ideas will be more fully developed later on. At this point, i 1 the effect of merger and acquisition on option ISDs will be discussed. The behavior of ISDs around merger and acquisition announcements is not I only a major determinant of call option returns and thus optionholders wealth but also has important implications for event studies in the equity market . Event studies in the equity market implicitly assume that risk 1 remains constant. Predicted returns are based on historical data from some base period. Increasing ISDs (i.e., stock volatility) would suggest that risk is increasing. More importantly, since ISDs can be 24 computed at a point in time and are correlated with stock betas, they can be used to adjust for increasing risk in the event period. This is discussed later on in this chapter. The Behavior of ISPs Around Merger and Acquisition Announcements The behavior of option ISDs around merger and acquisition announcements is important for a variety of reasons. First, it is inseparable from the price behavior of options. Stock volatility is one of the input variables for the Black-Scholes model. By examining the behavior of the ISDs it is possible to decompose changes in option prices into a component due to price changes in the underlying stock and a component due to changes in the underlying volatility. A second reason for examining the behavior of ISDs is that it provides an alternative measure of the information content associated with merger and acquisition announcements. The vast majority of event studies have attempted to measure the information content of some event by showing the expected return of the stock is affected. Patell and Wolf son (1979,1981) have pointed out that other moments of the stock price distribution may also be affected and thus serve as a measure of its significance. They used ISDs as an ex-ante measure of the informa- tion content associated with earnings announcements whose date is known . This study will determine if the second moment (stock volatility) of the stock return distribution is affected by merger and acquisition activity. The behavior of ISDs will be tracked around the announcement date for both the bidding and target firms in order to determine if there is a difference in the impact of the activity between the two 25 categories. It should be noted that merger and acquisition announce- ments are unexpected or at best partially anticipated. This fact distinguishes this study from the ones by Patell an Wolfson which dealt with earnings announcements on known dates. Another reason for examining the behavior of ISDs is that it may shed light on potential wealth shifts engendered by merger and acquisi- tion activity. Option theory suggests that common stock can be interpreted as an option. Agency theory suggests that there is an incentive for stockholders (see Jensen and Heckling 1976) to shift wealth from the bondholders by undertaking risky investm.ent projects. By undertaking investment projects which increase the variability of the firm's cash flows, the stockholders' can, in effect, gamble with the bondholder's money. This enriches the stockholders at the direct expense of the bondholders. Merger and acquisition activity can be regarded just like any other investment activity. Consequently, one might expect bidding firms to make acquisitions which tend to increase the variability of the firm's cash flows. Others, however, have argued that the opposite occurs. Levy and Sarnat (1970), Lewellen (1971) and Galai and Masulis (1976) have argued that combining the cash flows of two independent com.panies may reduce the probability of default and increase the market value of debt at the stockholders' expense. Even if this occurs, it is possible that managers act to neutralize (issue more debt) any such wealth shift. In any case, it is the variability of the firm's cash flow that is in question. A direct relationship, however, has been hypothesized in previous work (see Eger 1983). Consequently, the behavior of ISDs 26 around merger/acquisition announcements may be of value in analyzing whether these wealth shifts do, in fact, take place. ■Methodology The methodology used for analyzing ISD behavior is as follows. First the sample was stratified into two groups. The first group was composed of 52 bidding firms involved in a merger or acquisition. The second group was composed of 21 target firms involved in a merger or divestment. Base ISDs were obtained by "inverting" the Black-Scholes model using data forty days prior to the announcement date. It is assumed that the markets have not yet begun to reflect the merger and acquisi- tion activity at this point. If the 40th day prior to the announcement is a holiday or weekend, the first trading day afterwards is used. Dividends are assumed to be paid continuously and are adjusted for as suggested by Merton^ (1973). The stock and option prices are the first prices from the Berkeley option tapes after the stock price has changed once. The opening trade is eliminated in order to ensure the market has stabilized. ISDs are calculated in a similar manner for each company for each day in the event period. The event period ranges from five days prior to the announcement date to two days afterward. It should be noted that the announcement day is taken to be the date it first appeared in the Wall Street Journal . In many instances, the news was released during trading hours of the previous day. Dividends are adjusted for by using Merton's (1973) formula C = Se"ytN(di) - Xe'^^Nid-y) where dl = [ln(S/X^ + (r - y - 0T5a2)t]/aVt d2 = dl - oVt y = continuous dividend vield. 27 The impact of the merger and acquisition activity on option ISDs was measured by taking the difference between the ISD for each company for each day during the event period and the base ISD for each company SISDjt " ISDjt - ISDbj where 6ISD^^ = Change in ISD for company j on day t. (t = -5 to +2) ISD-^ = ISD for company j on say t ISDb^ = Base ISD for company j A t-test was run on the change in ISDs for each day in order to determine statistical significance: t = 6ISDj/(s2/N)"l/2 The results are given in Table 3.1. For each day in the event period the mean change in the ISD is given, the t-statistic and the probability (if significant at the lOZ level) of exceeding the absolute value of the t-statistic given there was no change in the distribution of ISDs between the base and event periods. The effect of changing ISDs on call prices was also investigated. For each company, for each day during the event period, the closing price of the option closest to the money with at least 30 days to maturity was obtained. The Black-Scholes Model was used to compute a call price on the same option using the base ISD but actual (market) stock prices. The percentage difference between the actual (market) call price and the theoretical base price obtained using base period ISDs in the Black-Scholes model was calculated for each company for each day in the event period 28 Table 3.1 Average Change in ISDs Between the Base and Event Period Bidding Firms ay Average t- Prob > ISD Change Statistic It! -5 -0.010678 -1.41 -4 -0.009359 -1.46 — s -0.002800 -0.39 -2 0.000765 0.12 -1 -0.001085 -0.17 -0.005835 -0.73 +1 -0.005354 -0.58 +2 0.000932 0.10 Target Firms Day Average t- Prob > ISD Change Statistic /t/ -5 0.025402 1.35 -4 0.021308 1.34 -3 0.033090 1.92 .0690 -2 0.034044 2.01 .0580 -1 0.048052 3.03 .0071 0.056132 2.39 .0266 +1 0.024384 1.53 +2 0.004447 0.24 29 where %&C^^^ = % Difference between the actual and the base call price for company j on day t C-!^ = Actual market call price for company j on day t Cb^|- = Base price obtained from using base ISD in the Black-Scholes Model for company j on day t. Since the observed (market) stock price is used to obtain the base call price (Cb^-j-), the difference between the actual and base call prices must be entirely due to the changing stock volatility. A t-test was run on the percentage deviation from the actual call prices in order to determine statistical significance t = %6Cjt / (s2 / N)"l/2 The results are given in Table 3. For each day in the event period, the mean percentage deviation is given, the t-statistic and the probability (if significant at the 10% level) of exceeding the absolute value of the t-statistic assuming there was no change between the base and actual market call prices. I-'-erpretation of Results As one might expect, the above two tables are very consistent. They may be regarded as opposite sides of the same coin. The change in ISDs for the bidding firm is small and statistically insignificant (at the 10% level) in all instances. Similarly, the percentage deviation of market prices from base prices is also small and statistically insignificant. The change in ISDs for the target firm are much larger than those of the bidding firm for corresponding days in the event period. Furthermore, the change is always positive and statistically 30 significant for days -3 through the announcement date (Day 0). The same observations hold for the percentage deviation in prices. These results are consistent with the hypotheses of option market efficiency. For the bidding firm there is no evidence that the merger and acquisition activity has any effect on the volatility of the underlying stock. The change in ISDs are very small and do not result in large, statistically significant changes in the call prices. There does not appear to be any changes in the ISDs or call prices before and after the merger and acquisition announcement. The target firms are definitely affected by the merger and acquisition acrivity. The average change in ISDs is over 5 percentage points in absolute terms on Day and is responsible for call price increases of ovex 12%. The market, however, starts to anticipate the merger and acquisition announcement as early as three days ahead of time. The change in ISD from the base level jumps from roughly 0.021 on day -4 to 0.033 on day -3.0 to -0.048 on day -1 to 0.056 on day 0. The percentage change in call prices follow a similar pattern. Immediately after the announce- ment is made public, however, ISDs and call prices quickly stabilize at close to their base levels. The deviation of the market from the base call price is only 0.009 for the target firms the day after the announcement . The results in Tables 3.1 and 3.2 also support the hypothesis that ISDs can be used to measure the information content of merger and acquisitions announcements. Studies in the equity market have shown that mergers do not greatly affect the expected return of the bidding firm stockholders. It would appear that the volatility of returns is 31 Table 3.2 Percentage Deviation Between Market and Base Call Prices Day Bidding Firms % Deviation t-Statistic Prob > /t/ -5 -4 -3 -2 -1 +1 +2 -0,009791 -0.016577 -0.058152 0.002362 -0.030124 ■0.021935 -0.021193 ■0.013851 0.48 -0.78 -1.11 0.12 -1.49 -1.05 -0.89 -0.55 Target Firms Day % Deviation t- Statistic Prob > Itl -5 0.035339 0.76 -4 0.037151 0.85 -3 0.067024 1.66 0.1133 -2 0.085629 1.74 0.0966 -1 0.126755 3.14 0.0056 0.058533 1.65 0.1146 +1 0.008906 0.10 +2 -0.047437 -0.83 32 also unaffected. Changes in the bidding firm ISDs are very small and statistically insignificant. Studies in the equity market have also shown that significant abnormal returns accrue to the target firm shareholders. The results here indicate these abnormal returns are accompanied by increased return volatility. Tt should be noted that the numbers in Table 3.1 are absolute changes from the base ISD. The percentage deviations from the base ISD would be much larger. Why does merger and acquisition activity have such a major impact of the second moment (variance) of the return distribution of the target firms? As mentioned earlier, results in the equity market have shown that most of the gain from merger activity is captured by the target firm shareholders. The rationale for this is that the takeover market is competitive. If a company has some unique aspect that other companies can exploit, it will find or have the potential to find a number of bidders. Competition among the bidding firms will drive the net present value of the investment to zero (see Mandelker (197A) and Jensen and Ruback (1983)). Consequently, the gains from merger and acquisition activity will be reaped by the target firm shareholders. Because of this, merger and acquisition activity could be expected to affect the volatility of the target firm's equity much more then that of the bidding firm's. Merger and acquisition activity is a more or less neutral event for the bidding firm shareholders. Target firm shareholders, however, are likely to be greatly affected. The impor- tance of merger and acquisition activity to the target firm share- holders combined with uncertainty over the terms of the agreement, whether alternative bidders will appear, whether the agreement will be 33 consummated, etc., should result in higher ISDs for the target firm options. Table 3.2 confirms this hypothesis. The average change for the bidding firms is negligible. The average change in ISD for the target firms is larger than that of the bidding firms for the corre- sponding day in all cases. In some instances, the change in the target firms' ISDs exceeds those of the bidding firms by more than an order of magnitude. This result warrants further comment. Event studies in the equity market have demonstrated time and time again that target firm shareholders reap abnormal returns as a result of merger activity. These abnormal returns, however, are accompanied by increased vola- tility as Table 3.2 shows. Thus, these "abnormal returns" may not truly be abnormal but merely reflect the increased uncertainty and riskiness engendered by the merger and acquisition activity. Instan- taneous or short-term adjustments for risk are difficult in the equity market since beta requires historical time series to estimate. The ISD of an option, however, can be determined at a point in time. Thus, an event study in the option market may afford a better measure of excess return. This point is explored more deeply in the next section. A final comment on the behavior of ISDs. It is interesting that the ISDs for both the bidding and target firms' revert back to their base level after the merger and acquisition announcement (see Table 3.2). It would appear that merger and acquisition activity does not result in permanent changes in the volatility of the underlying equity for either bidding or target firms. The evidence here does not support the hypotheses that wealth shifts between bondholders and stockholders 34 arises from merger and acquisition activity. This is counterintuitive. One would expect the post-announcement ISD to be function of the volatility of the underlying equity of both companies and their correlation. These results may be due to the sample selection process. Companies listed on the CBOE tend to be large com.panies. Thus, a merger and acquisition of $100 million may still be insignificant. In addition, large mergers or acquisitions are likely to take place between solid, established companies of relatively equal size. Thus, any conclusions concerning wealth shifts and merger and acquisition activity based on the data here must be interpreted with great care. The Behavior of Call Option Prices Around Merger and Acquisition Announcements Many of the reasons for examining the behavior of option prices around merger and acquisition announcements have already been discussed earlier. First, it provides a test of option market efficiency. Merger (and acquisition) negotiations involve many people such as investment bankers, lawyers, administrative personnel, etc. Word of impending mergers leaking to the financial market place has been amply demonstrated in the equity market (see Keown and Pinkerton, 1981). There is no reason why the same phenomenon should not occur in the option market. The price behavior of options around merger and acquisition announcements is important to anyone who intends to invest or speculate in options. Merger and acquisition activity is a major economic factor in our economy and is likely to remain so for some time. Anyone involved in options may be confronted with an unanticipated merger or acquisition announcement. Options by their very nature afford superior leverage to the underlying equity. Optionholders, per dollar invested. 35 are more affected by merger and acquisition activity than the equity- holders. In order to invest intelligently, potential optionholders (or sellers) need to have some idea of how merger and acquisition activity could potentially affect their wealth position. Another reason for analyzing the behavior of option prices around merger and acquisition announcements is that it may help to determine if this type of activity is an "event" from the standpoint of the bidding firm. As noted earlier, gains to the bidding share holders are small, possibly negative and statistically insignificant (see Chapter 2). It also appears that merger and acquisition activity has no effect on the volatility (second moment of the return distribution) of the bidding firm's equity. It is possible, however, that the option prices of the bidding firms might still measurably react to the merger and acquisition activity. An option can be interpreted as a leveraged position in the equity. The leverage aspect of options may make them more sensitive to events than the underlying equity. A shock or event that provides an insignificant abnormal return in the equity market might be magnified into an identifiable, significant abnormal return in the option market. Thus, it might be easier from a statistical standpoint to determine if merger and acquisition activity is an event to the bidding firm security holders. A final reason for examining the price behavior of call options is that this is the first study to apply the traditional event study methodology to the option market. The event analyzed here is merger and acquisition announcements. The methodology employed, however, has 36 general applicability. It can be applied to any event such as dividend or earning announcements. Methodology and results An event study attempts to measure the impact of some event on securityholders by comparing the actual, observed market returns to those predicted by some model. Ideally, these predicted returns should be the returns that would have occurred if the event (merger and acquisition activity) had not taken place. This study uses the Black- Scholes model to generate predicted returns. In a Black-Scholes framework, call option prices change when there is a change in the risk-free rate, the time to expiration, the exercise price, the stock price or stock volatility. In equilibrium, the actual, observed market price equals the theoretical, Black-Scholes price. Here the announcement effect is measured by the impact of the changing stock price and volatility on the option price. The observed call option price is compared to a predicted price generated by the Black-Scholes model that keeps the stock price and volatility constant. An event study in the option market is fundamentally different from the one in the equity market. Event studies in the equity market assume the return generating process is linear and that the true beta remains constant over time. As long as predicted returns equal actual returns on average, residuals should average out to zero over a large enough cross-sectional sample in the absence of some common disturbing event. This also justifies using an estimate of beta. The true beta is unobservable and must be estim.ated. If an unbiased estimate of beta is used, deviations from the true expected return will also offset and 37 residuals should average out to zero in the absence of a common disturbance. The return generating process in the option market, however, makes an event study inherently different from one in the equity market. A cursory examination of the Black-Scholes model shows it is highly non- linear. Even if unbiased estimators are used to obtain inputs for the model, equal deviations from the true parameters will not result in equal deviations from the true call price. Thus, residuals will be biased simply due to the estimation of the input variables. This issue has important implications for users of the Black-Scholes model and is analyzed at length in Chapter 4. Another difference between an event study in the two markets is that the uncertainty of an option is an explicit function of time. The uncertainty of an option with a short time to maturity is greater than the same option with a longer life. The Black-Scholes model incor- porates this time dependency and will be used for this study. The methodology used to examine the behavior of call prices around merger and acquisition announcements is as follows. First, as before, the sample was divided into bidding and target firms. A number of options with different exercise prices and maturities exist for a company on a listed exchange. One option was selected to avoid statistical dependence in the returns. The exercise price selected was the closest price to the stock price forty days prior to the announce- ment. It is assumed that the impending announcement will not be reflected in option prices at this point. The maturity selected will be the first expiration date at least thirty days after the event period. 38 The reason for these particular choices of exercise price and maturity is to mitigate problems with using the Black-Schoies formula. The Black-Scholes formula has been found to be less accurate for deep in-the-money or out-of-the-money options. Thus, an option near-the- money is used. The reason for insisting the option have at least 30 days to expiration is that the Black-Scholes model has been shown (see Manaster and Rendleman 1982) to be sensitive to its underlying assump- tions for options close to expiration. Once an option is selected according to this criteria, returns will be computed for each day in the event period. These returns will be matched with predicted returns computed from prices generated by the Black-Scholes formula. The predicted returns should be untainted by the merger and acquisition activity. Of the five input variables for the Black- Scholes model, only the stock volatility and stock price are likely to be affected. The obvious approach to estimating the stock volatility is to use historical stock returns from some base period. Another method is to "solve" the Black-Scholes formula for the implied standard deviation. ISDs reflect market expectations and should provide better estimates of future stock volatility than historical data. This has been confirmed by Latane and Rendelman (1976), Trippi (1977) and Chiras and Manaster (1978). Although a number of complex weighting schemes have been suggested, Beckers (1981) has demonstrated that using the ISD from the option nearest the money may work just as well. For this reason, the base ISDs computed in the previous section will be used to proxy the base volatility. The efficient market hypothesis suggests that the best estimate of tomorrow's stock price is today's stock 39 price. For this reason, the closing stock price 40 days prior to the announcement date (which is assumed to be unaffected by merger and acquisition activity) is used as the input stock price. Residuals will be computed for each company for each day in the event period "j.t = Rj,t - R'^j,t where U^,^ = residual for company j on day t J R j,|- - actual (observed) option return for company j on day t R*jjt ~ predicted option return for company j on day t Next daily average residuals will be com.puted to measure the impact of the merger and acquisition announcement for each day in the event period _ n U^- = 1/N .E,U. ^ ^ j=i J>t where U*. = average daily residual for day t N = number of observations Finally, cumulative average residuals (CARs) will be calculated to measure the total abnormal return accruing to the optionholders. t CAR^ = S U^ t=-4 The statistical significance will be measured by a t-test on the daily residuals 40 ^'t ' -^^ 7 n (u. ^ - e) 1 . , N - 1 Residuals for the bidding and target firm will, of course, be treated separately. The results are given in Table 3.3. For each day in the event period, the daily average residual, t-statistic, probability (if significant) of exceeding the absolute value of the t-statistic and CAR are given. Interpretation of results It is interesting to note that with the possible exception of the bidding firms' behavior on day-2, the results in Table 3.3 are consis- tent with the results in Tables 3.1 and 3.2. Merger and acquisition activity has a much larger impact on the target firm option holders than the bidding firm optionholders. The cumulative average residual is about 7.5% through the announcement day for the bidding firm options versus about 39% for the target firm. Abnormal returns for the target firm options are statistically significant two days and the day before the announcement. It would seem, however, that merger and acquisition activity is an event for the bidding firm option holders. The excess return of 6.4% two days before the announcement is highly significant. This is consistent with the ISD behavior of the bidding firms' options on day- 2. Although not statistically significant, the ISD does change sign and become positive (see Table 3.1). The issue of whether merger or acquisition, should be regarded as an event (having measurable impact) 41 Table 3.3 Abnormal Returns in the Option Market Around Merger and Acquisition Announcements Bidding Firms Daily Day Average t- Prob > Car Residual Statistic Itl Dav-4 0.004993 0.21 0.004993 Day-3 0.007201 0.37 0.012194 Day-2 0.064110 2.87 0.0059 0.076304 Day-1 0.015931 0.40 0.092235 Day -0.017628 -0.62 0.074607 Day+1 0.019649 0.74 0.094256 Day+2 0.022679 Tar Daily 0.92 get Firms 0.116935 Day Average t- Prob > Car Residual Statistic Iti Day-4 -0.015935 -0.52 . -0.015935 Day-3 0.033639 0.69 0.017704 Day-2 0.128971 1.75 0.0956 0.146675 Day-1 0.210493 2.68 0.0152 0.357168 Day 0.031266 0.45 0.388374 Day+1 0.017990 0.51 0.406364 Day+2 0.025705 -0.90 0.380659 42 on the bidding firm optionholders will be returned to in the next section. The above results, as might be expected, are consistent with the hypothesis of market efficiency. For both the bidding and target firms, the formal announcement is anticipated. After the merger and acquisition is made public, there are no excess returns. The "abnormal returns" in Table 4 are based upon the traditional event study methodology that has been used in the equity market. That is, the parameter(s) (beta in the equity market) for the model generat- ing the predicted returns are estimated using data from some base period free from the disturbing effects of the event (merger and acquisition) activity. The difference between the actual, observed market returns and the predicted returns is defined to be the excess or abnormal return. This excess return assumes that the risk (beta) does not change. In actuality, merger and acquisition activity may not benefit a stockholder even if abnormal returns are observed. These abnormal returns may be accompanied by increased risk engendered by the merger and acquisitionn activity. If risk were compensated for on a contin- uous basis, it is possible that the abnormal returns reported would disappear. This has not been done in the equity market since estimat- ing beta requires time series data over a relatively lengthy period of time. The issue is explored more fully in the next section. For an event study in the option market, it is not necessary to estimate beta. The relevant counterpart is the stock volatility for which the ISD can be used as a proxy. The ISD, however, unlike beta, can be computed at a point in time. This allows for a more complete 43 current estimate of predicted returns for event studies in the option market than in the equity market. In order to demonstrate this, the event study above was rerun for the target firms on Day -2 and Day -1 (which yielded abnormal returns). The only difference is that ISDs from the previous day (rather than 40 days prior to the announcement date) were used in the Black-Scholes model to generate predicted returns. That is, prices for day-3 were based on ISDs from day-4, prices for day-2 were based on prices from day-3 and prices for day-1 were based on ISDs from day-2. All other aspects of the study are identical. The results are shown in Table 3.4. The implication of these results is that abnormal returns reported in event studies to date may be overstated. Using the previous day's ISDs to reflect a more current measure of the stock volatility reduced the excess return on day-2 by almost three percentage points. Although there is no direct relation between a stock's volatility and beta, it would seem logical that merger and acquisition activity could have short run effects. If beta could be observed on a continuous basis so that equity returns could be properly adjusted for risk, abnormal returns might be substantially reduced or even eliminated. This is discussed in more detail in the next section. The behavior of option markets around merger and acquisition announcements This section extends the event study in the option market to the underlying equity. The reason for doing this is to compare the behavior of the two markets around the announcement of merger and acquisitions. There are two major reasons for doing this. Table 3.4 Target Firm Option Abnormal Returns Based On Previous Day ISDs Daily Day Average t- Prob > Residual Statistic t Day-2 0.099975 1.45 0.1617 Day-1 0.208600 2.49 0.0288 45 The first is that it places the option market results in perspec- tive. While the absolute level of abnormal returns is of interest in itself, it is important to compare the level of excess returns in the option and equity markets. An investor concerned with merger and acquisition activity would need to know the relative effects before he could properly allocate his resources between the two markets. The second reason for extending the event study to the underlying stocks is that the two markets may behave differently. There are two independent arguments for the hypothesis that merger and acquisition activity will be first manifested in the option (rather than equity) market. Options can be interpreted as leveraged positions in the underly- ing equity. The beta of an option is always greater than that of the underlying asset (stock). Thus, it is possible that the option market may be more sensitive to events than the equity market. In other words, although both markets may have received the same bit of informa- tion, the signal may be "magnified" and first apparent in the option market . It is also possible that the option market contains information that is not incorporated in the equity market prior to major corporate announcements. As mentioned previously, a call or put option can be duplicated by an appropriate stock-bond portfolio. Because of this, options have been viewed as "derivative" assets whose prices are completely determined by the underlying equity. The possibility that the option market may influence the equity market has received little attention. Information may first be processed in the option market and then filter to the equity market. 46 This issue has been investigated by Manaster and Rendleman U982). They advanced the intriguing hypothesis that the option market may play a key role in determining equilibrium stock prices. They argue that some investors may prefer to invest in the option rather than the equity market because of reduced transaction costs, fewer short selling restrictions and most importantly, superior leverage. These traders could push option prices out of equilibrium relative to the underlying stocks. Arbitragers would then intervene to restore equilibrium between the two markets. Manaster and Rendleman attempted to test their theory. They "inverted" the Black-Scholes model to solve for the implied stock price. The implied stock price was then used to predict future stock prices. They found some evidence that the option market contains information that is not incorporated in the equity market. Unfortu- nately, their results are very weak and fatally flawed by their reliance on non-synchronous data. The data used in this dissertation avoids this problem. In retrospect, Manaster and Rendlemans' lack of results is not surprising. Both the option and equity markets react to public information. Generally, one would expect both markets to adjust simultaneously to new public information. On any given day for any particular corporation there may not be and probably is not information that is not fully reflected in both markets. However, this may not be true prior to m.ajor announcements by corporations such as mergers or acquisitions. In this case, the option market could be expected to be particularly influential in determining stock prices. Keown and Pinkerton (1981) have argued that information 47 concerning impending mergers is susceptible to insider exploitation due to the large number of people typically involved in the negotiating process. They have attributed increased trading volume before the merger announcement to insider activity. An insider attempting to profit from knowledge of an impending merger would have an incentive to use options because of their leverage aspects. To quote Fischer Black (1975, p. 61), "Since an investor can usually get more action from a given investment in options than he can be investing in the common stock, he may choose to deal with options when he feels he has an especially important piece of information." Option prices can be expected ro contain more information than the equity market if non- public information is being exploited. If information regarding future mergers first reaches the financial markets through insider trading in options, merger activity may very well be reflected in the option market before the stock market. Methodology and results The standard event study methodology was applied to the equity market. Daily returns for each day in the event period were obtained from the Center for Security Price Research (CRSP) tapes. These observed market returns were then compared to mean returns . Mean returns were computed using returns for the sixty trading days prior to the base date forty days prior to the announcement date. Residual computation and analysis is as before. Residuals are calculated for each company for each day in the event period ^'j't ~ ^i,t ' '^i where U- ^ = residual for company j on day t 48 where U4 ^ = residual for company i on day t R-j ^ = actual equity return for company j on day t R-j = mean return for company j Next daily average residuals are com.puted to measure the impact of the merger or acquisition announcement for each day in the event period _ n U^ = 1/n E U.^. 3 = i Cumulative average residuals are also calculated to measure the total excess return accruing to the equityholder . Statistical significance of the residuals is measured as before by a t-test on the daily residuals. U, • Vn t = n (U - e )2 v' E -^ r^- n - i j = l The results are given in Table 3.5. For each day in the event period, the daily average residual, t-statistic and probability of exceeding the absolute value of the t-statistic, if significant, is given. Table 3.5 is consistent with other merger studies done in the equity market. Merger and acquisition activity has very little impact on the bidding firms. The largest daily average residual, although statistically significant at the 10% level is only 0.0044. For the target firms, a statistically significant daily average return of almost 0.04 was observed on day-1. The abnormal returns for the target firm equityholders is a little low compared to returns obtained in other merger studies. This 49 Table 3.5 Abnormal Returns In The Equity Market Around Merger and Acquisition Announcements Bidding Firms Day Day-4 Day-3 Day-2 Day-1 Day Day+1 Day+2 Daily Average Residual -0.001457 0.001275 0.004015 -0.002133 -0.007647 -0.003259 0.000562 t- Prob > atistic /t/ Car -0.65 -0.001457 0.50 -0,000182 1.71 0.0926 0.003833 -0.52 0.001700 -2.15 0.0362 -0.005947 1.26 -0.009206 0.22 -0.008694 Target Daily Average t- Day Residual Statistic Dsy-4 -0.006512 -1.68 Day-3 -0.002720 -0.50 Day-2 0.007597 1.07 Day-1 0.039875 +2.44 Day 0.000620 0.08 Day+1 -0.002300 -0.36 Day+2 0.000402 0.08 Prob I /t/ 0.0240 Car -0.006512 -0.008932 -0.001335 0.038540 0.039160 0.036860 0.037262 50 concerning impending mergers is susceptible to insider exploitation due to the large number of people typically involved in the negotiating process. They have attributed increased trading volume before the merger announcement to insider activity. An insider attempting to profit from knowledge of an impending merger would have an incentive to use options because of their leverage aspects. To quote Fischer Black (1975, p. 61), "Since an investor can usually get more action from a given investment in options than he can be investing in the common stock, he may choose to deal with options when he feels he has an especially important piece of information." Option prices can be expected to contain more information than the equity market if non- public information is being exploited. If information regarding future mergers first reaches the financial markets through insider trading in options, merger activity may very well be reflected in the option market before the stock market. Methodology and results The standard event study methodology was applied to the equity market. Daily returns for each day in the event period were obtained from the Center for Security Price Research (CRSP) tapes. These observed market returns were then compared to mean returns. Mean returns were computed using returns for the sixty trading days prior to the base date forty days prior to the announcement date. Residual computation and analysis is as before. Residuals are calculated for each company for each day in the event period "j't = Rj,t - Rj 51 is probably due to the sample. Companies listed on the CBOE tend to be large, established companies. The takeover market may not be as efficient for firms of this size. Relatively few companies have the resources to undertake an acquisition of this scope. This fact is reflected in the sample. Of the 21 target firms in the sample, seven are mergers. For the divestitures, abnormal returns may also be comparatively small due to the size of the firms involved. Although large in absolute terms, a $100 million divestiture for a company such as General Electric is likely to have very little impact. Although the pattern of abnormal returns is similar for both markets, the residuals in the option market tend to be much larger. For the bidding firms, cumulative average residuals were 0.074607 through the announcement day for the options vice -0.005947 for the equity. For the target firms, cumulative average residuals were 0.388374 and 0.039160 for the options and equity, respectively. The only puzzling feature in the above tables is the statis- tically significant excess return for the bidding firms options observed two days prior to the announcement date. The results in the equity market, however, are consistent. The average residual for day- 2, although small in absolute terms, is large compared to those of other days and is statistically significant. It should be noted that the data source used in the option and equity markets are independent. The Berkeley option tapes served as the basis for the option event study and the CRSP tapes for the equity. The results for day-2 are also not due to low priced options. A small price change on an option priced at less than a dollar could result in large returns that m.ight not actually be realizable. This 52 possibility was checked for by redoing the analysis for the bidding firm options on day-2 and the target firm options on day-1. This time, however, rerurns based on prices less than one dollar are eliminated. The results are given in Table 3.6. The daily average residual for the bidding firm does decline from about 6.4% to roughly A%. It is, however, still statistically significant. Eliminating the low priced options from the target firms actually increases the daily average residual. The results from this study support the hypotheses that merger and acquisition activity is first manifested in the option market. For the bidding firms in the equity market, the daily average residual is uniformly small. In the option market, however, there is a large jump between the daily average residual of 0,007201 on day-3 and 0.06AI10 on day-2. For the target firms, the evidence is more pronounced. In the equity market, the merger and acquisition activity is not evident until day-1. In the option market, the merger activity is definitely reflected by the excess returns on day-2 and arguably on day-3. The target firm ISDs, however, have started to react three days prior to the announcement. As noted earlier, abnormal returns were obtained for the target firms in the equity market (see Table 3.5). These abnormal returns, however, were based on historical data. Thus, an underlying assumption is that the risk (beta) does not change. In reality, merger and acquisition activity may be accompanied by increased risk that is not reflected in the base beta. If beta could be observed on a continuous basis so that equity returns could be properly adjusted for risk, abnormal returns might be substantially reduced or even eliminated. 53 Table 3.6 Selected Abnormal Returns with Call Prices Under $1.00 Eliminated Bidding Fii Day-2 ■ms Target Firms Day-1 Daily A/erage Residual t- Statistic Prob > Itl Daily Average Residual t- Statistic Prob > Itl 0.039593 1.98 0.0536 0.248540 2.76 0.0147 54 A number of attempts were made to adjust for risk in the equity market by exploiting the high correlation between a stocks volatility and beta. Unlike beta which requires time-series data, the ISD can be calculated at a point in time. Although there is no theoretical relationship between the ISD and a stock's beta, empirical relation- ships can be established. These relationships can then be used to adjust for the increasing risk due to the impending merger or acquisi- tion announcement. The methodology used to adjust the laevel of risk in the equity market during the event period involves regressing stock betas against their volatility. Daily returns for the target firms were regressed against the market (CRSP value weighted) index for the six months prior to the base (AO days prior to the announcement) date. This yielded the intercept for the market model and an unadjusted beta to conduct an event study in the equity market. Stock volatilities based on the daily returns were also calculated. The target firm betas were regressed against the volatilities to obtain the following relation B = 0.866764 + 19.48914--'' a R^ = 0.098 A similar relationship was obtained using annual data. Annual returns for the target firm were regressed against the market (CRSP value weighted) index for the thirty years 1952 to 1981. Stock volatilities based on this annual data were also computed. The annual betas were then regressed against the stock volatilities to obtain B = -0.061901 + 3.669232-- a R^ = 0.714 55 These relationships were used to adjust the beta for each day in the event period. The ISD was plugged into the equations above to obtain an adjusted beta. These adjusted betas were then plugged into the market model (based on the daily returns) to generate predicted returns. The standard event study methodology was then used to obtain the results shown in Table 3.7. The first colmnn is the residuals and associated t-statistics obtained from using an unadjusted beta, that is, the beta based on the six months of daily data. The second column shows the results obtained when the ISD is used to adjust the beta using the relationship between beta and a based on the annual data. The third coliamn shows the results when the ISD for each day in the event period is used to adjust the beta using the relationship based on the daily data. These results indicate the adjustments for risk were not success- ful. On day-1, the abnormal return are almost identical regardless of whether the unadjusted beta, adjusted beta based on annual return data or daily return data is used. Either the adjustment procedure is flawed or the level of risk did not change during the event period. An analysis of the data reveals a technical reason why the adjustment procedure did not work. In a CAPM framework, stocks must have an expected return greater than the risk-free rate. Ex-post, however, negative returns do occur. Many of the market returns on the day prior to the announcement date (day-1) were negative in this sample. The average market return is -0.000808. The practical effect of this is that adjusting beta upwards can result in larger abnormal returns (residuals) because of the data. If the market return is negative, increasing beta will only result in a 56 Table 3.7 Abnormal Returns for the Target Firms for Various Beta Adiustments Day Unadjusted Annually Daily Beta Adjusted Adjusted Beta Beta -4 -0.002448 -0.003664 -0.003431 (t = -0.59) (t = -0.89) (t = -0.81) -3 -0.002102 -0.001601 -0.001539 (t = -0.51) (t = -0.41) (t = -0.39) -2 0.005530 0.005232 0.005516 (t = 0.84) (t = 0.79) (t = 0.82) -1 0.032000 0.033300 0.033147 (t = 2.34) (t = 2.35) (t = 2.34) Q 0.001017 0.001048 0.001032 (t = 0.13) (t = 0.14) (t = 0.14) +1 -0.002665 -0.002597 -0.002729 (t = -0.66) (t = -0.64) (t = 0.26) +2 0.001301 0.000929 0.001190 (t = 0.28) (t = 0.19) (t = 0.26) 57 lower predicted return. This illustrated by the abnormal returns that result from the following adjustment to beta for day-1 Bg = B[(ISD(-1) - ISDb)/lSDb) + 1.0] • k where B^ = adjusted beta B = base beta obtained from six months daily data ISD(-l) = ISD on day-1 ISDb = base ISD k = an arbitrary scaler The results for k = 1, 1,3, 1.5, and 2.0 are shown in Table 3.8. Here we see that increasing beta has very little impact on the residuals. A larger beta results in a larger predicted return (smaller residual) impact for those companies for which the market return was positive. This is offset, however, by those companies for which the market return is negative. The magnitude by which beta would have to be increased in order to eliminated the abnormal returns can still be calculated. Adding 0.015 to the market returns on day-1 to make them positive and B-'.OIS to the company returns does not change the residuals but makes the adjustment process conform to theoretical expectations. The above regressions were rerun with the indicated adjustment. The results are given in Table 3.9. These results show that adjusting the base beta by the percentage change in the ISDs times a scaler of 1.40 reduces the abnormal returns to statistical insignificance. This suggests that the basic methodology used to adjust beta above is sound but needs to be applied to a larger sample where the average market return is positive. 58 Table 3.8 Abnormal Returns Obtained by Adjusting Beta by the Percentage Change in ISDs Times a Scaler (K) K = 1.0 K = 1.3 K = 1.5 K - 2.0 Day -1 0.033378 0.033793 0.034070 0.034751 (t - 2.34) (t = 2.35) (t = 2.35) (t = 2.33) 59 Table 3.9 Abnormal Returns Obtained by x'Vdjusting beta by the Percentage Change in the ISD and a Scaler (K) After Adding 0.015 to the Market Returns and B"'.015 to the Company Returns K = 1.0 K = 1.10 K = 1.20 K = 1.30 K = 1.40 Day-1 0.029318 0.027321 0.025323 0.023325 0.021327 (t = 2.19) (t = 2.05) (t = 1.91) (t = 1.77) (t = 1.62) (0.0422) (0.0552) (0.0720) (0.0939) (12.17) CHAPTER 4 VARIANCE BIAS AND NON- SYNCHRONOUS PRICES IN THE BLACK- SCHOLES MODEL One of the underlying assumptions of an event study in the equity market is that the return generating process is linear. As long as predicted returns equal observed (actual market) returns on average, residuals (abnormal returns) should also average out to zero. It is the common disturbance (event) that generates abnormal returns. This linearity of the return generating process also justifies using an estimate of beta. If an unbiasec estimator of beta is used, errors will tend to offset. The estimates of beta may be high or low but will average out in a large sample. Furthermore, the error in estimated returns and thus residuals will also average out to zero. The Black-Scholes model, however, is highly nonlinear. Thus, using an estimate for the input variables may result in a systematic bias. Even if an unbiased estimator is used for the input variables (most notably the stock volatility), errors from the true call price will not offset even in a large sample. The reason for this is that equal deviations from the true input parameters will not result in equal deviations from the true call price. This has implications far beyond that of conducting an event study in the options market. Applying the Black-Scholes model has an inherent bias due to the fact that the formula is non- linear and input variables must be estimated. The magnitude and direction of these 60 61 biases is of interest to any user of the Black-Scholes model. For this reason, the issue of bias in the Black-Scholes model arising from these sources is considered in a broader context rather than as a technical issue concerning event study methodology. This chapter has two sections. The first section deals with the bias that results in the Black-Scholes model from using a sample estimate of the variance with all other input parameters assumed to be known. The following section extends the analysis to uncertainty in the underlying stock price due to non-synchronous trading (or price quotes) between the option and equity markets. Variance Bias in the Black-Scholes Model The Black-Scholes model is by far the most widely used option pricing formula. In order to apply it, five input variables must be obtained: the stock price, exercise price, time to maturity, risk-free rate of interest and the volatility of the underlying stock. Of these variables, four are directly observable. Only the variance of the underlying stock returns needs to be estimated. Hull and White (1987) have analyzed the impact of cp- itself being stochastic on the call option value. In this paper, however, we assume that a^ is constant but its estimate, S'^, is a random variable. Classical methods of estimating the variance will bias the Black- Scholes model as Ingersoll (1975) and Merton (1976) have pointed out. To see this, define Z^ = Ln(l + R^) where R|. is the rate of return on the underlying stock in period t and assijme that Z^ is an independent, normally distributed random variable. The unbiased estimate, a^, of the variance of the stock returns is given by 62 n t=i - Z)2 §2 = = (4.1) N - 1 where N is the number of observations _ n Z = S Z^/N t=l While it is well known that S'^ is an unbiased estimate of a^, it is not true that E(C) = C where C is the value derived from the Black-Scholes formula with the true but unknown a^ and C is a random variable calculated by employing the Black-Scholes formula with the random variable S^. Let us elaborate this point. The Black-Scholes model is given by C = SgNCd^) - Ee'^tfj(^i2) ^ ^_2 where d^ = [InCSg/E) + (r + 0.5a2)t]/aVt d2 = dj_ - aVt and the sample estimate of C is given by C C = SQN(d^) - Ee"^%(d2) ^-3 where dj^ = [InCSg/E) + (r 4- 0.5s2)t]/sV t d2 = dj_ - sVt (recall that S is a random variable) It is obvious that E(C) ^ C for the following reasons. First, even if E(s2) = a2, E(S) ^ a and a is one of the inputs into the Black- Scholes formula. Second, even if E(S) = a (which it does not), E(C) ^ 63 C since a appears in the denominator of the formula and E(l/S) ^ l/o. Even if E(S) = a and E(l/S) = l/o, the model would still be biased due to its non-linearity. Equal deviations from the the true a^ would not result in equal deviations from the true option price. Analyzing the gap between E(C) and C is difficult. One has to evaluate the following difference LnCSg/E) + (r+0.5s2)/sVt LnCSg/E) + (r-0. 5S)t/s2Vt ■O.SZ^ -rt -0.5Z2 E(C) - C = Sg J 1/V2TT e dz - Ee J 1/V2tt e dz LnCSo/E) + (r+0.5a2)t/aVt Ln(Sn/E) + (r-0.5o2)t/aVt -0.5Z2 -rt -0.5Z2 -Sq J 1/V2TT e dz + Ee J 1/V2tt e dz A closed-form solution to the first two integrals is extremely complex since S, a random variable, appears in the upper bound. Boyle and Anathanarayanan (1977) used numerical integration to approximate the above integrals and investigated the case of an option expiring in 90 days. In this paper, we provide an alternative approach by using simulation. Sample estimates, S'-, of the stock volatility, o" , are generated and used to compute option prices using the Black- Scholes formula. These prices are then compared to the theoretical value determined by using the true o" in the Black-Scholes formula in order to measure the bias induced. This is repeated for options with 64 various maturities. The dispersion of sample call prices from the theoretical value is also investigated. Methodology and Results The effect of using a sample estimate of the variance in the Black-Scholes model was analyzed using simulation analysis. For this purpose, an option with the following characteristics was chosen. These parameters were representative of IBM options in the early 1980 's. Note that the true stock volatility is assumed known. Stock price = $68,125 Risk-Free Rate = 0.1325 of Interest True Standard = 0.4472 Deviation of Stock Returns Time to Maturity = Various Exercise Price = Various The simulation is based on the well known relationship 'iTi'.veen the sample and true variance 9 S is distributed as a Chi-square with N-1 degrees of freedom which for this analysis is assumed to be fifty-nine. This implies that the sample variance was estimated using sixty observations. One thousand Chi-square deviates were obtained using the International Mathematical and Statistical Library (IMSL) computer program. The sample variance was then computed for each Chi-square observation for input into the Black-Scholes formula. For each exercise price, one thousand call 65 prices using the sample variances obtained from simulation were calculated and the average computed. Options with five, sixty, and two hundred seventy days to maturity were examined. The results are given in Table 1. The theoretical price assxaming the true variance is known is given for each exercise price. The exercise price changes in five percent increments from the given stock price of $68,125. The average simulation price is the mean of the thousand generated call prices. The percentage bias is calculated by % bias = '^'^h^o^^^tical price-average simulation price) * 100 theoretical price Note that a positive bias is associated with average simulation prices less than the theoretical Black-Scholes prices. These results show a definite bias exists. While mean simulated prices do deviate from theoretical Elack-Scholes prices, however, the differences are small. In most cases, the average simulation price is within a few cents of the theoretical price. The largest difference is approximately eight cents. The percentage bias is also sm.all. For the options with 60 and 270 days to expiration, it is always under one percent. While biases over one percent do occur for the option with five days to maturity, they are at prices so low as to be economically meaningless . A few observations on the nature of the bias between the average simulation value and the theoretical value should be made. First, A downward bias exists in most cases. The average value obtained from simulation is less than the theoretical value for all nine exercise prices for the options with sixty and two hundred seventy days to expiration. For the five day option, the theoretical price exceeds the 66 Table 4.1 Theoretical Call Price and Average Simulation Call Price T = 5 Days to Maturity Exercise Theoretical Average Simu- Percent Price Price lation Price Bias 5A.500 13.7178 13.7157 0.01523 57.906 10.3184 10.3175 0.00872 61.313 6.9418 6.9427 -0.01253 64.719 3.7987 3.7966 0.05503 58.125 1.4799 1.4701 0.66084 71.531 0.3669 0.3636 0.89129 74.938 0.0549 0.0568 -3.49790 78.344 0.0050 0.0060 -20.16123 81.750 0.0003 0.0005 -50.71423 T = 60 Days to Maturity Exercise Theoretical Average Simu- Percent Price Price lation Price Bias 54.500 15.1807 15.1806 0.00040 57.906 12.3118 12.3038 0.06482 61.313 9.7241 9.7056 0.19035 64.719 7.4747 7.4468 0.37366 68.125 5.5917 5.5583 0.59802 71.531 4.0735 4.0402 0.81773 74.938 2.8926 2.8639 0.99112 78.344 2.0055 1.9846 1.04311 81.750 1.3596 1.3474 0.90314 T = 270 Days to Maturity Exercise Theoretical Average Simu- Percent Price Price lation Price Bias 54.500 20.9884 20.9614 0.12868 57.906 18.7896 18.7513 0.20132 61.313 16.7597 16.7107 0.29198 64.719 14.9000 14.8419 0.39013 68.125 13.2070 13.1416 0.49526 71.531 11.6748 11.6044 0.60293 74.938 10.2950 10.2220 0.70870 78.344 9.0591 8.9858 0.80924 81.750 7.9562 7.8849 0.89591 67 average simulation price for five exercise prices. In the other four cases, the bias is extremely small amounting to less than one cent. The bias is largest in absolute terms for the options with longer maturities. However, there is no systematic relationship when the bias is expressed in percentage terms. When the bias is expressed in percentage terms, the bias for the sixty day option is smaller than that of the two hundred seventy day option at low exercise prices but larger at high relative exercise prices. For an option of a given maturity, the bias is more pronounced at high exercise prices. This holds true regardless of whether the bias is expressed in absolute or percentage terms. This makes intuitive sense. At low exercise prices most of an option's value is due to its intrinsic worth. At high exercise prices more of the option's value can be attributed to the volatility of the underlying stock. Conse- quently, the estimate of the variance becomes more important. The results in Table 4,1 are encouraging to users of the Black- Scholes model. The bias in a large sample is small. This does not guarantee, however, that using a sample estimate of the variance will not severely degrade the applicability of the Black-Scholes model. Sample call prices might each differ from the theoretical price by a great amount. In a large sample these individual errors might offset so that the average error was small. The dispersion of the sample call prices from the theoretical value is also crucial. For this reason, average simulated prices were generated on the same IBM option as before only using A, 6, 8, 10, 15 and 30 runs instead of a thousand. The results are given in Table 4.2. As before, options with 5, 60 and 270 days to expiration were examined. For each 68 Table 4.2 Average Simulated Values and Bias for Various Sample Sizes Maturity = 5 Days Exercise Price = $54.50 Theoretical Price = $13.7178 Number of Average Simulat ions Simulation Price 4 13.7178 6 13.7178 8 13.7178 10 13.7178 15 13.7178 30 13.7178 Percent Bias 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Maturity = 5 Days Exercise Price = $68,125 Theoretical Price = $1,4799 Number of Average Simulat ions Simulation Price 4 1.5181 6 1.4626 8 1.4516 10 1.4526 15 1.4608 30 1.4669 Percent Bias -2.5812 1.1690 1.9123 1.8448 1.2906 0.8785 Maturity = 5 Days Exercise Price = $81,750 Theoretical Price = $.0003 Number of Average Percent Simulat: Lons Simulation Price Bias 4 0.0005 -66.6667 6 0.0004 -33.3333 8 0.0003 0.0000 10 0.0003 0.0000 15 0.0003 0.0000 30 0.0004 -33.3333 69 Table A. 2 (continued) Maturity = 60 Days Exercise Price = $54.50 Theoretical Price = $15.1807 Number of Average Simulat ions Simulation Price 4 15.2367 6 15.1680 8 15.1528 10 15.1526 15 15.1618 30 15.1742 Percent Bias -0.3689 0.0837 0.1838 0.1851 0.1245 0.0428 Maturity = 60 Days Exercise Price = $68,125 Theoretical Price = $5.5917 Numbe r of Average Siinul ations Simulation Price 4 5. 7214 6 5.5328 8 5.4955 10 5.4980 15 5.5266 30 5.5473 Percent Bias -2.3195 1.0533 1.7204 1.6578 1.1642 0.7940 Maturity = 60 Days Exercise Price = $81.75 Theoretical Price = $1.3596 Number of Simulations Average Simulation Price Percent Bias 4 6 8 10 15 30 1.4633 1.3239 1.2949 1.2962 1.3159 1.3355 -7.6272 2.6258 4.7588 4.6632 3.2142 1.7725 70 Table 4.2 (continued) Maturity = 270 Days Exercise Price = $54.50 Theoretical Price = $20.9884 Number of Average Simulat ions Simulation Price 4 21.1675 6 20.9231 8 20.8727 10 20.8753 15 20.9101 30 20.9429 Percent Bias 3.9112 0.3112 0.5513 0.5389 0.3731 0.2168 Maturity = 270 Days Exercise Price = $68,125 Theoretical Price = $13.2070 Number of Average Simulat ions Simulation Price 4 13.4635 6 13.0913 8 13.0177 10 13.0244 15 13.0789 30 13.1198 Percent Bias -1.9421 0.8760 1.4333 1.3826 0.9699 0.6603 Maturity = 270 Days Exercise Price = $81.75 Theoretical Price = $7.9562 Number of Average Simulat ions Simulation Price 4 8.2374 6 7.8293 8 7.7485 10 7.7559 15 7.8157 30 7.8606 Percent Bias -3.5344 1.5950 2.6105 2.5175 1.7671 1.2016 71 of these maturities, exercise prices of $54.50, $68,125 and $81.75 were selected. The percent bias is calculated as before 5. The theoretical Black-Scholes price is also given for each option. These results show that the dispersion of option prices from their theoretical values due to using the sample variance is not great. The largest absolute difference is about $0.25. In general, the percentage bias is usually less than 2%. The major exception is for the out-of- the-money option with five days to maturity. This is due to the insignificant theoretical call prices (less than $0.01) associated with this option. The same observations concerning the behavior of the bias for the large sample (1000 runs) experiments apply to the small sample experi- ments. The bias is generally positive (theoretical price exceeds average simulated price). When the bias is negative, it is almost always associated with the smallest number of simulations (4). Again, the percentage bias is usually smallest at low exercise prices and becomes larger as the exercise price is increased. Non-synchronous Prices and the Black-Scholes Model Many investment decisions involving options are based on closing stock and option prices or other non-sychronous sources of data. Since the option market is much thinner than the stock market, these prices are often based on trades from different times of the day. The stock price prevailing at the time of the last option trade may be signifi- cantly different from the closing price at the end of the day. Conse- quently, using this stock price in the Black-Scholes model may cause options to appear mispriced as Trippi (1977), Chiras and Manaster (1978), Galai (1977) and Bookstaber (1981) have pointed out. 72 Here the raispricing of options that can occur due to the non- simultaneity or stock and option quotations and using a sample estimate for the variance of the underlying stock returns in the Black-Scholes model is examined. An option is constructed for analysis and its theoretical value is calculated assuming the input variables including the relevant stock price and true volatility a^, are known. This value is compared to call prices generated with the same parameters (includ- ing the true assumed volatility) only varying the input stock price from the assumed true stock price in order to measure the effects of nonsimultaneous stock and option quotations. The additional bias resulting from using a sample estimate of the variance is measured by simulation analysis. For each stock price, sample estimates, 3--, of the stock volatility, o^ , are generated and used to compute option prices using the Black-Scholes formula. These prices are then compared to the theoretical price determined by using the true variance, o^, and true (synchronous) stock price in order measure the bias due to the combination of the two factors. The methodology and results are describe below. Methodology and Results Simulation analysis was used to m.easure the effects in the Black-Scholes model of using a sample estimate of the variance in conjunction with nonsimultaneous stock and option quotations. For this purpose, an option with the following characteristics was chosen. These parameters are representative of a typical option traded on the Chicago Board Option Exchange in the mid 1980 's. Note that the true stock volatility and stock price are known. 73 Stock Price = $50,000 Risk-Free Rate = 0.1000 of Interest True Standard = 0.3500 Deviation of Stock Returns Time to Maturity = Various Exercise Price = $50,000 The effect of nonsiir.ultaneous stock and option prices alone on the Black-Scholes model was measured by varying input stock price in 1/8 increments from the true stock price of $50,000. For each stock price between $49,000 and $51,000 the Black-Scholes value was computed using the parameters listed above including the true assumed variance of 0.3500. The combined effects of nonsimultaneous price quotations and using a sample estimate of the variance was analyzed by simulation. The simulation is based on the relationship between the sample and true variance didcusssed earlier 2 S N . 1 ^ A. 4 S^ is distributed as a Chi-square with N-1 degrees of freedom which for this analysis is assumed to be twenty-nine. This implies that the sample variance was estimated using thirty observations. One thousand Chi-square deviates were obtained using the International Mathematical and Statistical Library (IMSL) computer program. The sample variance was then computed for each Chi-square observation for input into the Black-Scholes formula. For each exercise price, one thousand call prices using the sample variances obtained from simulation were 74 calculated and the average computed. Options with five, sixty, and two hundred seventy days to maturity were examined. The results are given in Table 4.3. For each stock price, the Black-Scholes value is given based on the true variance of 0.3500. This gives a measure of the mispricing that can occur to nonsimul- taneous price quotations. For each of these stock prices, the average simulation price is also given. The average simulated price is the mean of the thousand generated call prices obtained with that exercise price and estimates of the variance. The percentage bias of these values from the theoretical value is also given. The percentage bias is calculated by % bias = ^^^^"^^^^^^^ price-average simulation price) * 100 theoretical price Note that a positive bias is associated with average simulation prices less than the theoretical Black-Scholes prices. These results indicate that making investment decisions involving options on the basis of nonsynchronous price data must be made with great care. Even when the stock price is off by only an eighth the observed call price will deviate from its theoretical price by over one percent. For short maturities, using a stock price that deviates from the true stock price by one dollar can results in call prices that are over 50% off from the true value. The error due to using a sample estimate of the true variance is small in comparison to that caused by using nonconteraparenous stock prices. For stock prices above the true value, the two errors are offsetting. For stock prices below the true stock value, the two errors reinforce one another. 75 Table 4.3 Mispricing in the Black-Scholes Model Due to Nonsimultaneous Stock and Option Quotations and Using a Sample Estimate for the Variance of the Underlying Stock Returns T = 5 Days to Maturity Theoretical Price = 0.843231 Stock Black-Scholes Average Percent Bias Percent Price Price With Simulation Due to Non- Bias Due to True Variance Price Simultaneous Quotations Both Effects 51.000 1.455809 1.452143 -72.6465 -72.2117 50.875 1.369338 1.365278 -62.3918 -61.9103 50.750 1.285629 1.281119 -52.4646 -51.9298 50.625 1.2046Q5 1.199766 -42.8558 -42.2820 50.500 1.126509 1.121297 -33.5944 -32.9762 50.375 1.051239 1.045770 -24.6679 -24.0193 50.250 0.978912 0.973244 -16.0906 -15.4184 50.125 0.909561 0.903781 -7.8662 -7.1807 50.000 0.843231 0.837410 0.0000 -0.6903 49.875 0.779953 0.774134 7.5042 8.1943 49.750 0.719757 0.713988 14.6430 15.3271 49.625 0.662537 0.656968 21.4288 22.0892 49.500 0.608398 0.603052 27.8492 28.4832 49.375 0.557251 0.552217 33.9148 34.5117 49.250 0.509110 0.504414 39.6240 40.1809 49.125 0.463882 0.459599 44.9875 45.4954 49.000 0.417516 0.500117 50.0117 50.4644 76 Table 4.3 (continued) T = 60 Days to Maturity Theoretical Price = 3.135864 Stock Black-Scholes Average Percent Bias Percent Price Price With Simulation Due to Non- Bias Due to True Variance Price Simultaneous Quotations Both Effects 51.000 3.726805 3.708286 -18.8446 -18.2540 50.875 3.649992 3.631251 -16.3951 -15.7975 50.750 3.574020 3.555066 -13.9724 -13.3680 50.625 3.498869 3.479729 -11.5759 -10.9655 50.500 3.424468 3.405258 -9.2033 -8.5907 50.375 3.351058 3.331654 -6.8623 -6.2436 50.250 3.278503 3.258919 -4.5486 -3.9241 50.125 3.187067 3.187067 -2.2607 -1.6328 50.000 3.135864 3.116100 0.0000 0.6303 49.875 3.065887 3.046021 2.2315 2.8650 49.750 2.996780 2.976843 4.4353 5.0711 49.625 2.928482 2.908547 6.6132 7.2489 49.500 2.861113 2.841156 8.7617 9.3980 49.375 2.794615 2.774673 10.8821 11.5181 49.250 2.728973 2.709085 12.9754 13.6096 49.125 2.664169 2.644415 15.0419 15.6719 49.000 2.600462 2.580659 17.0735 17.7050 T = 270 Days to Maturity Theoretical Value = 7.302824 Stock Black-Scholes Average Percent Bias Percent Price Price With Simulation Due to Non- Bias Due to True Variance Price Simultaneous Quotations Both Effects 51.000 7.948135 7.909295 -8.8364 -8.3046 50.875 7.866165 7.827100 -7.7140 -7.1791 50.750 7.784515 7.745256 -6.5959 -6.0584 50.625 7.703323 7.663871 -5.4842 -4.9439 50.500 7.622467 7.582793 -4.3677 -3.8337 50.375 7.541931 7.502134 -3.2742 -2.7292 50.250 7.461836 7.421933 -2.1774 -1.6310 50.125 7.382185 7.342033 -1.0867 -0.5369 50.000 7.302824 7.262574 0.0000 0.5512 49.875 7.223953 7.183511 1.0800 1.6338 49.750 7.145445 7.104862 2.1550 2.7108 49.625 7.067305 7.026569 3.2250 3.7829 49.500 5.989562 6.948733 4.2896 4.8487 49.375 6.912291 6.871284 5.3477 5.9092 49.250 6.835295 6.794231 6.4020 6.9643 49.125 6.758818 6.717631 7.4493 8.0132 49.000 6.682646 6.641387 8.4923 9.0573 77 Conclusion In empirical tests of the black-Scholes model, one normally employs ex-post estimates of o"^ since a^ itself is unknown. While the sample variance is an unbiased estimate of a", the derived option value (which is a random variable) is a biased estimate of the true Black- Scholes value. The effects of this bias were analyzed by simulation. The true variance was assumed to be known and sample estimates generated by using a Chi-square distribution. One thousand sample variances and their associated call prices were obtained in each case. The average call price was calculated and compared to the theoretical Black-Scholes value. This process was performed on options with various maturities and exercise prices. The results show that using a sample estimate for the variance in the Black-Scholes model results in a downward bias. The average simulation price was less than the theoretical price for all options with 60 and 270 days to maturity. For the 5 day option, the average simulation price was less than the theoretical price for 5 of the 8 exercise prices. When an upward bias was observed, it was not economi- cally significant. The downward bias was also evident in the small sample experiments. Sample call prices were generated in the same manner previously described only using fewer trials. Average simula- tion prices were computed using 4, 6, 8, 10, 15 and 30 runs. The average call prices generated by simulation were usually less than the theoretical Black-Scholes price for six or more runs. The differences between the average call prices generated by simulation and the 78 theoretical values were small. The percentage biases were also small except for deep-out-of-the-money options close to expiration. The effect of non- synchronous prices was also investigated. If the input stock prices deviate from the true stock price by only 1/8, the mispricing ranged from roughly 1% for the 270 day option to approximately 7% for the 5 day option. The additional error due to using an estimate of the variance was relatively small. CHAPTER 5 SUMMARY AND CONCLUSIONS This dissertation investigated the behavior of options around merger and acquisition announcements. A variation of the traditional event study methodology was applied to the option market in order to determine the abnormal returns accruing to the bidding firm and target firm optionholders. The event study was then extended to the under- lying equity and the results between the two markets compared. In both the equity and option market, the effect of merger and acquisition activity was most pronounced for the target firms. The cumulative average residuals for the bidding firms in the equity market through the announcement date were close to zero. For the target firms, they were close to 4%. The corresponding CARs in the option market were 7.5% and 38.8%, respectively. The abnormal returns for the target firms in the option market are surprisingly large. Abnormal returns accruing to the optionholder are over 10 times as large as those accruing to the equityholders . The is due is not only the leverage effect in options but the fact that the stock volatility is increasing as well. Merger and acquisition activity can be expected to have a larger impact on the volatility (second moment of the return generating function) of the target firms than of the equity firms. Event studies in the equity market have shown that most of the gains from merger activity are captured by the target firm shareholders. The rationale 79 80 for this is that the takeover market is competitive. If a company has some unique aspect to exploit, it will find or have the potential to find a number of bidders. Competition among the bidding firms will drive the net present value of the investment to zero. Because of this, merger and acquisition activity should be expected to affect the volatility of the target firms' much more than the bidding firms'. Merger and acquisition activity is a more or less neutral event for the bidding firm shareholders. Target firm shareholders are much more likely to be greatly affected. The importance of merger and acquisition activity combined with uncertainty over the terms of the agreement, whether alternative bidders will appear, whether the agreement will be consummated, etc., should result in higher ISDs for the target firms. This hypothesis was confirmed. The change in the ISDs between the event period and base date for the bidding firms was not significant. The changes were small and statistically insignificant. The target firms, however, had large statistically significant changes in the ISDs. The effect of changing stock volatility on option prices was also examined. Option prices in the event period were compared to those using the Black-Scholes model using the current stock price but the base ISD. The results showed that changing stock volatility was an important factor in the abnormal returns reaped by the target firm optionholders. The results of this study also suggest that merger and acquisition activity is first reflected in the option market. The target firm ISDs started to increase and were statistically significant 3 days 81 before the announcement. Target firm option returns had started to increase and were statistically significant 2 days before the announce- ment. Target firm stock returns, however, did not significantly increase until the day prior to the announcement. Bidding firm option returns were economically and statistically significant two days before the announcement. Bidding firm stock returns were very small through the announcement date although they were statistically significant 2 days before the announcement. These results have practical implications for investors. If someone anticipates a company is about to announce a merger or acquisi- tion, they would reap much greater returns by purchasing options rather than the stock. Furthermore, they would be substantially better off by purchasing the target firm option rather than that of the bidding firm. This dissertation analyzed two issues involving the event study methodology. The first was the proper adjustment for risk in the equity market. Predicted returns have usually been based on data from some base period. The traditional event study methodology, thus, implicitly assumes that risk remains constant. It is far more likely that risk is actually changing due to the event (merger and acquisition activity). Abnormal returns would thus be overstated. Empirical relationships between the ISD (stock volatility) and beta were developed. These relationships were then used to adjust beta during the event period. Although conceptually sound, the results were disappointing due to a technical factor. The market return for many of the companies was negative. This resulted in smaller predicted returns (larger residuals) when larger betas were plugged into the market model. 82 The second major issue involves event studies in the option market. The Black-Scholes model is non-linear. Unbiased estimators for the input variables will still bias the results since equal deviations from the true input parameter value will not result in equal deviations from the true call price. Simulation analysis was used to measure the magnitude of this effect. The results indicate that although caution must be used in interpreting the results of an event study that uses the Black-Scholes model to generate predicted returns, the error is usually small. ij REFERENCES ; Asquith, R., "Merger Bids, Uncertainty, and Stockholder Returns," 1 Journal of Financial Economics , April 1983, 51-83. j Asquith, R. , R. Bruner, and D. 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Yoder was born on June 18, 1953, at Fort Monmouth, New Jersey. He received his Bachelor of Science degree in mathematics in 197A from the State University of New York at Albany. He then went on to obtain an M.A. in economics in 1975 from the same university. Mr. Yoder entered the Navy in the Nuclear Power Program. He served on board the U.S.S. Dwight D. Eisenhower and made one Mediterranean deployment. After leaving the Navy, he completed his MBA at the State University of New York at Albany before entering the Ph.D. program at the University of Florida. I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. 1 < u c/-"^..'^'^" 1 Haim Levy, Chairman-'' Walter J. Mather ly Professor of Finance T ce-rtify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. / /t,... Roy Cium Professor of Finance, Insurance, and Real Estate I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Sanfor/'V. Berg ^^ Profei^'sor of Economics This dissertation was submitted to the Graduate Faculty of the Depart- ment of Finance, Insurance, and Real Estate in the College of Business Administration and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy- Dean, Graduate School December 1988